Make an object stop interacting with fluid
I assume that you're using the original Elbeem fluid simulator.

With particle systems, you can isolate them by placing them on different layers.
However, with the Elbeem fluid simulator, it basically ignores the layers, and
treats everything as being on the same layer. So moving the obstacle to a different layer is not an option.

Unfortunately, (unless I'm overlooking something), the eye/camera icons that are next to the 'Fluid' button in the Physics tab > 'Enable Physics for' section appear to do nothing (at least for the Fluid Obstacle Object). The eye/camera icons in the Outliner only effect the visibility of the fluid object in the 3DView/Render respectively.
It would be great if they worked in a similar fashion to particles; then this would be very simple to do.

I tried scaling the obstacle glass/mug (to isolate it from the fluid),
and then moving it outside the domain.
However, in each case, the Elbeem fluid simulator seemed to work up until the
point where the obstacle was moved outside the domain. It didn't crash, it just seemed to stop working.

This is probably a bug, but since development on the original fluid simulator has ceased, and development effort is instead being directed to the MantaFlow simulator; you currently will have to work with what you have.
More information on the Blender implementation of Mantaflow at:
https://blenderartists.org/t/lets-talk-about-mantaflow/644346

and more information on the Mantaflow framework:

http://mantaflow.com/

Another option may be to look into the Flip Fluid Add-on by RLGuy
(I'm not that familiar with the add-on, but he did present some disappearing box type demo videos) It's a paid add-on, approx. $US 76. More details at:
https://blenderartists.org/t/flip-fluids-addon-a-liquid-fluid-simulation-tool-for-blender/702503

The method that seemed to work, was adding vertex keys to the obstacle (using a
Shell proxy object) and then moving the obstacle (while still keeping its
center point within the domain) such that only the obstacle's vertice were
outside of the domain. (This might also work with scaling and moving the obstacle, but I didn't try it).

When you add keyframes for vertex keys, you need to check the 'Export Animated Mesh'
option for the fluid and the Obstacle objects. (This isn't necessary for loc/rot/scale
keyframes).

Here's a blend file in case I forgot to mention some details:



Select the fluid domain from the Outliner,
Switch to the Physics tab in the Properties Area, and
Press Bake.